I would add some triangulation trusses to the box frames - stop it twisting etc.

If you were really good at carpentry there is no reason the base could not be made from timber, it would mean very tight joints and good design but the forces to resist for machining wood are not massive so i see no reason it could not be done. Cheaper in wood? I doubt it? Easier to build - not for me as i dislike wood and like metal but for a carpenter???

Anyways, that frame needs triangulation or it will wobble each time the spindle changes direction rapidly.